Using the equation of state PV = nRT; show ...

NCERT Class XI Chemistry States of Matter Solutions

Question : 3 of 23

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Using the equation of state PV = nRT; show that at a given temperature density of a gas is proportional to gas pressure P.

Solution:

According to ideal gas equation for ‘n’ moles of a gas, PV = nRT

But , n =

\frac{\text{Mass of the gas }(m)}{\text{Molar mass }(M)}

or P =

\frac{nRT}{V}

or P =

\frac{mRT}{MV}

[m/V = d density of the gas)]

∴ P =

\frac{dRT}{M}

or d =

\frac{MP}{RT}

or P α d

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